1. Field of the Invention
This invention relates to the control of piezoelectric and other scanners, and more specifically to scan control for scanning probe microscopy and other fields requiring a precision scanning stage.
2. Discussion of Background
Precision scanning stages are required by disciplines including scanning probe microscopy, beam lithography, and others. A common form of scanner for these applications is the piezoelectric scanner. The piezoelectric scanner comes in a variety of forms--single crystals, bimorphs, multilayer piezoelectric stacks, and tube scanners, for example. For all of these configurations, a voltage is applied across the piezoelectric elements and the position of some part of the piezoelectric scanner moves with respect to another part that is held fixed. This motion is used to scan samples, probes, lenses, etc., for a variety of purposes. Such scanners are often used to produce motion of the probe over the sample. However, motion of the sample stage with a fixed probe is equivalent for many applications and is also often employed.
Another kind of scanner is an electrostrictive scanner made typically out of PMN (lead-magnesium-niobate).
A very important area of application for such scanners is the field of scanning probe microscopes. In a scanning probe microscope such as the scanning tunneling microscope (STM) or the atomic force microscope (AFM), a probe is scanned across the surface of a sample to determine local properties of the surface such as topography or magnetic field strength so that these properties can be displayed for viewing. Alternately, the sample can be scanned relative to a fixed probe. Some of these microscopes, for example, the STM and AFM, have been constructed with the ability to resolve individual atoms. The scanner that provides the motion is usually a piezoelectric device adapted for moving in all three dimensions, i.e., the XY-plane and in the vertical (Z-axis) direction. Such three dimensional scanners have been built from discrete piezoelectric elements or from single tubes with internal and external electrodes segmented in a way to allow translation in all three dimensions (Binnig and Smith, Review of Scientific Instruments, Vol. 57 pp. 1688-89, (1986) and U.S. Pat. No. 4,087,715).
Images of the sample are usually created by scanning the probe over the sample in a so-called "raster" pattern, in the same way that an electron beam is used to create a television picture. For example, the probe is scanned at a high rate in the X-direction, back and forth across the sample, and at a low rate in the perpendicular (Y) direction. Data about the height, magnetic field or other local properties are collected as the probe is moved over the surface. To create such a scan pattern, it is necessary to apply scan voltages to the electrodes on the piezoelectric scanners. In the simplest case, where the piezoelectric sensitivity can be assumed to be constant, triangle waves may be applied to the X and Y electrodes to produce a linear raster pattern.
To resolve movement of a probe on the atomic scale, the scanning mechanism must be stable and accurately movable in increments on the Angstrom scale. Piezoelectric scanners have been widely used as such a stable and accurate scanning stage. In addition, there is great interest in scanning stages that have such precision and stability, but also have the ability to scan very large ranges, often over 100 microns, or to do small scans at various locations over a large field, at large offsets from the rest position. A system which must remain stable to 0.1 Angstrom and scan linearly over 100 microns is operating over a dynamic range of 1:10,000,000.
For small translations, piezoelectric scanners operate in a linear and reproducible way. That is, the displacement is proportional to the applied voltage. Thus at small amplitudes and for short times a piezoelectric transducer can be accurately described by its rest position, and its sensitivity, dX/dV. Unfortunately, piezoelectric scanners acquire a number of unwanted behaviors for translations on the micron scale and larger. At large scan voltages, the scanner's response can depend nonlinearly on the scan voltage and scan frequency. Also, in multiple axis scanners, there may be a coupling between the separate scan axes. The result is that a scan voltage applied to one axis may change the resulting motion on another axis. These unwanted behaviors in the piezoelectric response will mean that at large amplitudes, a linear signal applied to the piezo electrodes no longer produces a linear scan.
In addition to non-linearities and coupling, there may be other unwanted behaviors that make the scan pattern asymmetric when driven by a symmetric scan voltage. For example, piezoelectric scanners exhibit hysteresis such that as the direction of the applied voltage changes at the end of a scan, the position of the moving part of the piezoelectric scanner does not trace out its previous path. This is because the piezoelectric response to a scan voltage (sensitivity) is a function of the previous voltage history. Additional problems are caused by slow drifts in position caused by "creep." "Creep" is long term drift in position due to previous scan voltages applied to the scanner. There are also other drifts in the position of the scanner caused primarily by temperature variations and stresses in the scanner and its mounting hardware.
All of these effects conspire to make it difficult to create distortion-free scans for scan ranges larger than roughly 1 micron. In the field of scanning probe microscopes, it is desirable to accurately control both the scan size and pattern, but also to control the position relative to the sample where an image is being obtained. Deviations from linear scans make these accurate measurements difficult. The nonlinear scans also present similar problems in the use of scanning stages in other areas of application.
One possible solution to the hysteresis problem is to apply linear triangular voltage patterns to the electrodes, let the piezoelectric material scan in a non-linear manner and take Z data spaced evenly in time (but not space). After the data is recorded, the correct X,Y the positions of the Z data must be computed using calibration data for the scanner, and then the data is interpolated to construct Z(X,Y) for an equally spaced array in X and Y. This open loop scan control technique employing linear scan and image correction requires extensive calibration of the nonlinear and hysteretic behavior of each piezoelectric scanner during the manufacturing process. It is difficult to produce images in real time using this method, because many calculations are required after the data has been collected, This approach is described by Gehrtz et al in U.S. Pat. No. 5,107,113.
Barrett in U.S. Pat. No. 5,210,410 describes a related open loop method using position sensors which do not require extensive calibration of the scanner parameters. Instead, the position of the probe (or sample) is recorded from the sensor data at many points along the scan, along with the probe deflection data. Barrett describes several limitations of this method including the large amount of data which must be stored, inferior images resulting from the interpolation process, and the inability to measure very small position changes.
Elings et al in. U.S. Pat. No. 5,051,646 disclose another approach to solving the linearity problem by employing open loop scan control with a non-linear scan voltage. In this approach, nonlinear voltage patterns are applied to the electrodes to drive the piezoelectric scanner linearly with time by applying a nonlinear scan voltage. This open loop method preserves the inherent accuracy, low noise and high frequency response of the piezoelectric actuator for nanometer scale scans. For larger scans, in the 1 to 100 micron range, this approach has the difficulty of requiring detailed data concerning the behavior of each particular piezoelectric scanner, and therefore requires extensive calibration of each scanner in the manufacturing process.
Recently, several inventors have implemented closed loop scan control using position sensors that measure the motion of a piezoelectric scanner while it is scanning. Information from these position sensors is used to provide a feedback signal so that the scanners may be driven in a linear manner, with reduced effects of creep and hysteresis for scans in the 1 to 100 micron range. Alternately, the measurements from the position sensors may be used to correct data that has been acquired by an open loop scan. These sensors have been based on scanning a light pattern over a position sensitive photodiode as described in U.S. Pat. No. 5,172,002 and U.S. Pat. No. 5,196,713 by Marshall and previously by Barrett et al (Review of Scientific Instruments, Vol. 62, pp. 1393-99, June 1991) and his U.S. Pat. No. 5,210,410. In this patent Barrett clearly describes the limitations of the closed loop approach, stating ". . . for scans smaller than about 500 Angstroms the noise in the scan caused by the feedback system (dominated by the sensor noise) begins to noticeably degrade the image quality." Barrett also discusses stability problems inherent in a high gain closed loop precision motion control system.
Other position sensors have been used including optical interferometers (for example see Charette et al, Review of Scientific Instruments, Vol. 63, pp. 241-248, Jan. 1992) and capacitive sensors (Griffith et al, Journal of Vacuum Science and Technology B, Vol. 8, pp. 2023-27, Nov./Dec. 1990). In addition closed loop commercial piezoelectric scanning stages have been available since 1980 with capacitive sensors (from Queensgate), and also linear variable differential transformers (LVDTs, from Physike Instrumente). A variety of other position sensors are commercially available. In U.S. Pat. No. 4,314,174, Wing et al. describe the use of piezoelectric drive elements to dither an element in a laser gyroscope, with strain gauges being used to measure the dither and then feeding back this signal to control the drive elements, a standard closed loop control scheme.
Operation under closed loop control has been performed in the prior art in the following way. As depicted in simplified form in FIG. 1, a position sensor 40 is used to measure the instantaneous position of a scanner 30 carrying a probe tip 32 and a scan generator 10 generates a reference signal that describes the desired scan pattern. An error amplifier 12 produces an error signal proportional to the difference between the position sensor signal and the reference signal. The error signal is differentiated as indicated at 16 and integrated by integrator 14. Then the derivative, the output of the integrator, and a signal directly proportional to the error signal are summed at node 18 and directed to scanner 30. Thus the motion of the probe is under the continuous control of data from the sensor. A linear position sensor results in linear scan motion, but the inherent noise in the sensor introduces noise in the scan motion. If the sensor is non-linear, then the scan will be non-linear even under closed loop control, but could be corrected with a nonlinear reference signal.
In these closed loop systems, the scan reversal at the end of a linear scan is caused by abruptly reversing the slope of the reference signal. The sudden change in direction leads to a large error which takes time for the system to correct. The prior art control methods which rely on integration of the error signal to achieve an accurate linear scan take longer to recover control after reversal since the transient error is stored by the integral. This effect causes the motion to be non-linear at the reversals. The conventional closed loop control also fails to anticipate the special scan voltage requirements of piezoelectric transducers discussed by Elings et al in U.S. Pat. No. 5,051,644. In the closed loop system the appropriate transducer scan voltage is only generated after position errors exist and have been detected by the sensor. Typically, the error signal is electronically integrated to generate the scan voltage pattern. For a raster scan pattern, this same process is duplicated in both the scan axes. In the prior art, the type of feedback is fixed during manufacture and independent of scan parameters.
Unfortunately, it is difficult to find a sensor that matches well the operating dynamic range and bandwidth requirements of many piezoelectric scanners. Piezoelectric scanners used in scanning probe microscopes may have scan ranges of more than a hundred microns, yet need to be able to resolve detail on the subnanometer-scale. For scanning probe microscopes it is often desirable to operate with a dynamic range of about 10.sup.6 and a bandwidth of greater than 1 kHz.
While position sensors used in the prior art work acceptably for large scale scans, most do not have sufficient resolution to control accurately scans on the nanometer scale. Commercially available piezoelectric scanners with capacitive sensors or LVDTs have a quoted resolution of around 1-10 nm in the bandwidth required. Since atomic scale scans may be only 1 nm square, this resolution is clearly inadequate. If the system is operated with feedback for such small scans, the noise from the sensor will be introduced into the scan pattern of the scanning probe microscope and hence into the images. Using the prior art feedback systems, the only way to reduce the influence of the sensor noise on the scanning system is to reduce the speed of the feedback loop. This limits either the speed or the accuracy with which the scanner can be moved. Unfortunately for scanning probe microscopes, most users wish to speed up the scan for the small scans to reduce the effect of 1/f noise in the probe detection electronics and to minimize the effect of mechanical drift and transducer creep. So the requirements do not match the prior art approaches.
In the few cases where sensors can be optimized to provide subnanometer resolution, the sensors usually lack the dynamic range to also measure motions on the 100-micron scale. Optical interferometers are a very appealing sensor for a scan control system since they are self calibrating based on the wavelength of light used. Also, since the output is periodic, they have potentially infinite dynamic range (the sensor can measure infinitely large position shifts by counting an arbitrarily high number of periods). The periodicity is some fraction of the wavelength of light, typically a few hundred nanometers. Since scanning probe microscopes and other modern scanning systems require motions on a much smaller scale, it has been insufficient in the prior art to simply count successive periods.
This has been solved in the prior art by interpolating the periodic signal to measure displacement smaller than the fundamental period. Commercial interferometers are available from Zygo Corporation and Hewlett-Packard among others that claim a resolution of around 1 nm. To be successful, this type of interpolation requires extreme care in the construction of an optical system. These complex devices are very expensive and are not easily adapted to scanning systems such as scanning probe microscopes.
Potentially useful position sensors such as capacitive sensors may have an accurately known response function that is highly non-linear. Such sensors can not be used directly in conventional control systems without some form of linearization. Both sensors and transducers may mix motion in X, Y, and Z. Obtaining pure single axis motion may require scan voltages on all three transducers. Sensing a pure single axis position may require data from all three sensors. Such undesirable crosstalk adds to the difficulty of conventional feedback control systems.
In the prior art, one commercial solution to the problem of a noisy position sensor has been to turn off the scan feedback control when the scan size was reduced below the effective measurement range of the sensor, i.e. for scan sizes below about 2 microns. There are serious drawbacks to turning the feedback off. First, there is no longer any control over the scan size. In addition, the transition between so-called closed-loop (feedback on) and open-loop (feedback off), may result in an offset in the position of the scanner. This can make it difficult to localize and then "zoom in" on an object of interest in a scanning probe microscope. Another disadvantage to turning the feedback off at small scans is that there is no longer any correction for "creep." "Creep" and other forms of drift are perhaps the largest source of distortions at small scan sizes, so turning off the feedback altogether is an unattractive alternative.